Question

In a series LR circuit X_L = R and power factor of the circuit is P₁. When capacitor with capacitance C such that X_L= X_C is put in series, the power factor becomes P₂. The ratio `"P"_1/"P"_2` is ______. 

विकल्प

• `1/2`

• `1/sqrt2`

• `sqrt3/sqrt2`

• 2:1

Answer 1

In a series LR circuit X_L = R and power factor of the circuit is P₁. When capacitor with capacitance C such that X_L= X_C is put in series, the power factor becomes P₂. The ratio `"P"_1/"P"_2` is `underlinebb(1/sqrt2)`. 

Explanation:

Given that power factor of the circuit is P₁ when X_L = R

P₁ = `"R"/(sqrt("R"^2+("X"_"L"-"X"_"C")^2))=1/sqrt2`   (∵ X_C = 0)

Power factor of the circuit is P₂, when X_L = X_C

P₂ = `"R"/(sqrt("R"^2+("X"_"L"-"X"_"C"))^2)=1`

So, we have `"P"_1/"P"_2=1/sqrt2`